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# Tag Info

### Why not use the convolution theorem for explicit timestepping?

This is a linear PDE, and so while this technique works here, it would not work for any nonlinear PDE. Often times when people are solving these equations it is to get experience with common solution ...
• 2,089

### What is the advantage of using a particular RK Scheme?

You're looking only at the errors themselves and not other properties of the solution. There are sometimes good cases to consider lower-order schemes because they better preserve important ...
• 10.3k
Accepted

### Numerically computing the advection equation

I see several issues: The DFT computed with fft puts the zero mode at the beginning of the array, and if you want to compute the derivative, it is necessary to ...
• 11.4k
Accepted

### What is the advantage of using a particular RK Scheme?

There are lots of different properties which can be found in different time stepping schemes of the same order of accuracy: Different stability properties. While it may not appear that way with the ...
• 2,794

### Why do we have to resort to Higher order schemes for solving the 1-D advection equation/ continuity equation?

There is a difference between the requirements for a hyperbolic pde like $$u_t + a u_x = 0$$ and for a purely parabolic pde like $$u_t = u_{xx}$$ Suppose the solutions are smooth and you ...
• 3,028

### Advection equation with finite difference: importance of forward, backward or centered difference formula for the first derivative

Okay. Let's begin with the first situation. Your equation is: $$\frac{\partial f}{\partial t}+v\frac{\partial f}{\partial x}=0\tag{1}$$ $\textbf{Previous comments}$ There are plenty of webs that ...
• 1,648
Accepted

### More Smearing with decreasing timestep in advection problems

You solve the 1D-advection equation with $c$ a constant velocity: $$\frac{\partial u}{\partial t} + c\frac{\partial u}{\partial x}=0~~~~~~~~(1)$$ When you discretize this equation (with an explicit ...
• 629
Accepted

### When is it safe to ignore the diffusion term in an advection-diffusion equation?

The stationary equation you show transports information from the right to the left via the advection term; it also diffuses slightly. If you switch off the diffusion term altogether, then you only ...
• 55.7k
Accepted

• 3,028